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Calligraphy Brush Rendering (pen_type 60 & 61)

Physical Model

Both pens simulate a chisel-nib (broad-edge) calligraphy pen. The nib is a flat edge held at an angle; stroke width varies with the angle between the stroke direction and the nib orientation.

Key difference between the two pens:

Property Pen 60 (Brush A) Pen 61 (Brush B)
Thick when Stroke parallel to tilt azimuth Stroke perpendicular to tilt azimuth
Chisel formula |cos(stroke_dir - nib_angle)| |sin(stroke_dir - nib_angle)|
Min width fraction 18% of max 35% of max
Visual character Sharp hairline transitions Broader, softer variation

This corresponds to two nib orientations rotated 90 degrees from each other: pen 60's nib edge is aligned with the tilt direction, pen 61's is perpendicular to it.

Tilt Data

  • tilt_x: Pen azimuth, 256 units = full circle. Raw values wrap at 0/255; must be unwrapped with unwrap_8bit() before use.
  • tilt_y: Pen elevation, 256 units. Typical range 15-34. Not currently used in the width model (minimal measured effect on stroke width).
  • Nib angle: nib_angle = tilt_x * (2*pi / 256)

Width Formula

nib_w     = thickness * 0.95 * (pressure / 4095) ^ 0.5
chisel    = |cos(stroke_dir - nib_angle)|    # pen 60
          = |sin(stroke_dir - nib_angle)|    # pen 61
min_frac  = 0.18 (pen 60) or 0.35 (pen 61)
half_width = nib_w * (min_frac + (1 - min_frac) * chisel) / 2

Fitted by comparing .note stroke data against device-exported output. Typical RMSE on straight sections is ~0.3–0.6px.

Rendering Method

Device export: Filled polygon (closed path with ~5x more segments than input points). No per-segment strokes. The outline naturally expands at turns/corners.

Our approach: fill_stroke_outline() (in src/lib.rs) builds a variable-width polygon from per-segment quadrilaterals with round end caps. This reproduces the device behavior:

  • No circle artifacts (unlike per-segment drawLine with round caps)
  • Natural width expansion at turns
  • Start-of-line taper (quadratic ramp over first 8 points)

Smoothing

Three EMA (exponential moving average) filters ensure smooth output:

  1. Nib angle (alpha=0.15): Removes sensor jitter in tilt_x
  2. Stroke direction (alpha=0.3): Stabilizes tangent direction, especially at near-zero velocity
  3. Width (alpha=0.25): Prevents abrupt width jumps between consecutive points

Stroke direction uses wider central differences (window=3 points each side) before EMA for additional stability.

Known Limitations

  • Gold width measurements at turns are inflated by polygon fill geometry, making precise model fitting difficult at those locations
  • The tilt_y (elevation) component is not modeled; it may contribute a small width scaling effect
  • Our polygon outline doesn't exactly match the device's tessellation algorithm (5x segment expansion), but is visually close